How to reproduce a smartphone cover material with some specific reflection patterns
This is really just a supplement to Nicola's answer: my approach was to control the Anisotropic Rotation with a grad something like this:

simple

And a simple, dark, slightly blue-tinted glossy material, (roughness around 0.1).

resulting in this kind of response to peak light-sources in an HDR environment.



These are the nodes: I'm not knowledgeable enough in this area to justify them -  I've a feeling changing Anisotropic Rotation is equivalent to  rotating tangent space, bar some mapping, but how it's done in the Principled shader is something I have to look up.